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Q: If a triangle has two angles of equal measure that are each twice as large as the third measure what is the angles of the triangle?

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No but the sum of the squared sides will equal the square of the hypotenuse using Pythagoras' theorem for a right angle triangle

Angles having the same measure in degrees irrespective of how large the arms of one are compared to another are said to be congruent angles

Suppose the two acute angles are A and B degrees, where A = 3B. then A+B = 90 (since the sum of all three angles is 180) that is, 3B+BA=90 or 4B=90 => B=22.5 and then A= 3*22.5 = 67.5

The 4 to 1 ratio of the two acute angles can be restated as the larger acute angle is four times as large as the smaller acute angle. Since the sum of all angles in a triangle equal 180 degrees, the sum of the two acute angles will be equal to 90 degrees. The remaining 90 degrees are found in the right angle present in all right triangles. If we divide the 90 degrees of the acute angles by 5 (to get the five parts of our ratio) and ascribe 4 of those parts to the largest acute angle we can find the size of that angle by multiplying (90 / 5) x 4 = (18) x 4 = 72. Therefore the largest acute angle is 72 degrees and the smaller acute angle is 18 degrees for a total of 90 degrees. Answer: 72 degrees

Place the two large triangles next to each other so that their hypotenuses together make the long parallel side of the trapezoid. Place the medium triangle between the two large triangles with its hypotenuse along the edge of one of the large triangles. Place one of the small triangles between the medium triangle and the other large triangle with its hypotenuse along the edge of the medium triangle Place the square between the large triangle and the small triangle so that its edges are along side the small triangle and the large triangle. Finally place the parallelogram between the square and the medium triangle (toughing both) to finish the isosceles trapezoid. The seventh piece,. the final small triangle, which is not used, can be placed on top of the parallelogram (with its hypotenuse touching) to create a large triangle,. An Isosceles trapezoid can also be formed from all 7 pieces - take the large square formed by all the pieces except the two large triangles (as above if the large triangle is completed), and put the two large triangles on opposite sides to complete the isosceles trapezoid.

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90 degrees. This is an isosceles right triangle, standing on its hypotenuse.

This traingle is an equilateral traingle: which consists of all the three sides and angles to be congruent. The angles inside the triangle, just like any normal traingle, add up to be 180 degrees. The opposite of this traingle is the Scalene triangle which has all the three sides to be Uncongruent and has different angles. All the angles of ALL traingles still add up to 180 Degrees. The Isoceles triangle consists of two equal sides and one extravagantly large one side. Therefore, because of the previous properties, an isosceles traingle has two congruent angles and usually one obtuse or acute angle. The last triangle, the right triangle, has one right angle. It is the only triangle that is capable with triginomical ratios and the Pythagorean Theorem.

No but the sum of the squared sides will equal the square of the hypotenuse using Pythagoras' theorem for a right angle triangle

Angles having the same measure in degrees irrespective of how large the arms of one are compared to another are said to be congruent angles

Suppose the two acute angles are A and B degrees, where A = 3B. then A+B = 90 (since the sum of all three angles is 180) that is, 3B+BA=90 or 4B=90 => B=22.5 and then A= 3*22.5 = 67.5

Isosceles triangles are not always equal. Some are large some are small, some have two long sides that are equal, and some have two short sides that are equal. Every isosceles triangle has two sides that are of equal length; that is what makes it isosceles.

To find the measure of an angle, you need to know the size of the entire angle and the other angles within the angle. Then, you subtract the smaller, known angles from the entire, large angle and you should get the measure of the missing angle.

The sum of the 3 interior angles of any triangle ... no matter how large or small ... is always 180 degrees. This rule has no connection to the perimeter of the triangle. The perimeter may be one inch, less than one inch, 10 miles, more than 1,000 miles, etc., and the sum of the interior angles is always the same 180 degrees.

The 4 to 1 ratio of the two acute angles can be restated as the larger acute angle is four times as large as the smaller acute angle. Since the sum of all angles in a triangle equal 180 degrees, the sum of the two acute angles will be equal to 90 degrees. The remaining 90 degrees are found in the right angle present in all right triangles. If we divide the 90 degrees of the acute angles by 5 (to get the five parts of our ratio) and ascribe 4 of those parts to the largest acute angle we can find the size of that angle by multiplying (90 / 5) x 4 = (18) x 4 = 72. Therefore the largest acute angle is 72 degrees and the smaller acute angle is 18 degrees for a total of 90 degrees. Answer: 72 degrees

By historical convention a complete circle is 360 degrees, so if you take a point on a straight line and rotate until you face the other way the total angle is 180 degrees. Now if you take any two parallel lines, any distance apart, and mark a point anywhere on one line, and two points anywhere on the other line, then by varying these two lines and three points you can form any shaped triangle by joining up the three points. Now because the lines are parallel there is no angle between them, so a straight line drawn from one to the other will provide two identical angles rotated 180 degrees about. Call these two identical angles A. Now if you take a new line from one of the intersections to a new point on the other parallel line the same applies and we will call the two new identical angles B. If you draw this out you will have a triangle with a base with angles A & B and for the sake of convention we will call the remaining angle at the peak of the triangle C. The total angle at the peak of the triangle enabling one of the parallel lines to rotate and face the other way is, as we have said, 180 degrees but is also equal to C plus the rotated angles A and B. therefore A+B+C = 180 Degrees which is the same as your three angles in the triangle. ( It's much easier with diagrams). Or, you can work simpler like this: In a piece of paper draw a conveniently large scalene triangle ABC. Write 1 under the vertex A, 2 under the vertex B, and 3 under the vertex C (these numbers represent respectively the measure of angles A, B, and C). Cut the paper, and on another piece of paper point the three vertices A, B, and C. Connect these three points, and write the corresponding numbers 1, 2, and 3 respectively at vertices A, B, and C. Take the triangle and put the vertex C at the point A, A at C, and point B. Connect point B with others, and write the corresponding numbers under the corresponding vertices. Take the triangle and put the vertex C at the point B, the vertex B at A, and point A. Connect point A with others, and write the corresponding numbers under the corresponding vertices again. You can see that a straight angle is formed, whose measure is equal to the sum of the angles 1 + 3 + 2. Since the measure of a straight angle is equal to 180 degrees, then we say that the sum of the angles of a triangle is eaqual to 180 degrees (m A = 1) + (m B = 2) + (m C = 3) = 180 degrees.

A = 60 B = 20 C = 140 This can have a large number of answers.

Congruent angles have the same measure. congruent Kenpachi54 improve answer: Actually, angles don't have to be congruent just to have the same angle measurements A has a right angle is 90 degrees. even if there is a small right angle and a large right angle you know they are both 90 degrees because ALL right angles are 90 degrees, so there is really no name for it.

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